Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions

Details Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions Thermodynamics and collapse of self-gravitating Brownian particles in D dimensions

2002-04-14

arxiv.org/abs/cond-mat/0204303v1

Phys.Rev. E66 (2002) 046133

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.66.046133

We address the thermodynamics (equilibrium density profiles, phase diagram, instability analysis...) and the collapse of a self-gravitating gas of Brownian particles in D dimensions, in both canonical and microcanonical ensembles. In the canonical ensemble, we derive the analytic form of the density scaling profile which decays as f(x)=x^{-\alpha}, with alpha=2. In the microcanonical ensemble, we show that f decays as f(x)=x^{-\alpha_{max}}, where \alpha_{max} is a non-trivial exponent. We derive exact expansions for alpha_{max} and f in the limit of large D. Finally, we solve the problem in D=2, which displays rather rich and peculiar features.

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